How does Manhattan and Euclidean distance combine to control grease pencil input?
On this picture from Wikipedia green is Euclidean distance , rest - Manhattan distances. If the square was 10 by 10, then  Mathattan distance is 20, Euclidean sqrt(200), so around 14. So Euclidean distance  will be the real distance the mouse traveled, Manhattan - the number of pixels it travelled. Although it seems Blender uses the number of pixels per axis (probably taking maximum rather than summing them). In this case Manhattan distance will be 10.